The tracking performance of linear motor (LM) positioners is subject to payload uncertainty and external time-varying disturbances. Conventional robust controllers typically employ a high control gain that is substantially greater than the known a priori upper bound of the disturbance to ensure tracking error convergence. The main disadvantage of those controllers lies in that when the disturbance decreases, the control input is often overly generated, which then results in undesired control chattering effect or even actuator saturation. To overcome this problem, this article develops a robust tracking controller based on barrier function adaptive sliding mode (BFASM) for the LM positioners. The main benefits of BFASM are twofold: first, the controller is designed without the need for any disturbance information; second, its control gain is adaptively adjusted in terms of the amplitude of disturbance and, thus, leads to decreased control input when the disturbance becomes small. Furthermore, a modified barrier function (MBF) is proposed for applications with actuator saturation. It is proved that both the BFASM and MBF-based controllers can ensure the convergence of the tracking error into a prespecified neighborhood of zero in finite time. Experimental results on a real LM positioner demonstrate the superior properties of the developed controllers in comparison with two existing robust control schemes.

中文翻译：

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基于障碍函数自适应滑模的直线电机定位器跟踪控制

直线电机 (LM) 定位器的跟踪性能受有效载荷不确定性和外部时变干扰的影响。传统的鲁棒控制器通常采用高控制增益，该增益远大于已知的扰动的先验上限，以确保跟踪误差收敛。这些控制器的主要缺点在于，当扰动减小时，往往会过度产生控制输入，从而导致不希望的控制颤振效应甚至执行器饱和。为了克服这个问题，本文为 LM 定位器开发了一种基于障碍函数自适应滑动模式 (BFASM) 的鲁棒跟踪控制器。BFASM 的主要好处有两个：首先，控制器的设计不需要任何干扰信息；其次，它的控制增益根据扰动的幅度进行自适应调整，因此当扰动变小时会导致控制输入减少。此外，针对致动器饱和的应用提出了改进的势垒函数 (MBF)。证明了基于 BFASM 和基于 MBF 的控制器都可以确保跟踪误差在有限时间内收敛到预先指定的零邻域。与两种现有的鲁棒控制方案相比，真实 LM 定位器的实验结果证明了所开发控制器的优越特性。